###
DOI:
Journal of Software:2006.17(4):729-739

二维Logistic映射的动力学分析
王兴元,骆超
(大连理工大学,电子与信息工程学院,辽宁,大连,116024)
Dynamic Analysis of the Coupled Logistic Map
WANG Xing-Yuan,LUO Chao
()
Abstract
Chart / table
Reference
Similar Articles
Article :Browse 3354   Download 3497
Received:April 22, 2004    Revised:May 31, 2005
> 中文摘要: 对二维logistic映射的动力学研究有助于认识和预测更复杂的高维非线性系统的性态.利用解析计算和实验分析相结合的方法揭示出:(1) 参数空间中二维logistic映射发生第一次分岔的边界方程;(2) 二维logistic映射可按倍周期分岔和Hopf分岔走向混沌;(3) 二维logistic映射的吸引盆中周期和非周期区域之间的边界是分形的,这意味着无法预测相平面上点运动的归宿;(4) Mandelbrot-Julia集的结构由控制参数决定,且它们的边界是分形的.
Abstract:Dynamic analysis of the coupled logistic map redounds to know and predict the characteristics of high-dimension complex nonlinear system. Using the method combining calculation and experiment, the following conclusions are shown: (1) The boundary equation of the first bifurcation of the coupled logistic map in the parameter space is given out. (2) Chaotic patterns of the coupled logistic map may emerge out of double-periodic bifurcation and Hopf bifurcation, respectively. (3) The boundary between periodic and non-periodic regions in the attraction basin of the coupled logistic map is fractal, which indicates the impossibility to predict the moving result of the points in phase plane. (4) The structures of the Mandelbrot-Julia sets are determined by the control parameters, and their boundaries have the fractal characteristic.
文章编号:     中图分类号:    文献标志码:
基金项目:Supported by the National Natural Science Foundation of China under Grant No.60573172 (国家自然科学基金); the Superior College Science Technology Research Project of Liaoning Province of China under Grant No.20040081 (辽宁省教育厅高等学校科学技术研究计划) Supported by the National Natural Science Foundation of China under Grant No.60573172 (国家自然科学基金); the Superior College Science Technology Research Project of Liaoning Province of China under Grant No.20040081 (辽宁省教育厅高等学校科学技术研究计划)
Foundation items:
Reference text:

王兴元,骆超.二维Logistic映射的动力学分析.软件学报,2006,17(4):729-739

WANG Xing-Yuan,LUO Chao.Dynamic Analysis of the Coupled Logistic Map.Journal of Software,2006,17(4):729-739